The aim of this research paper is to systematically present an optimal control of a dc servomotor for the airflow measurement in both the magnitude and the direction. During measuring airflow, the dc servomotor drives a paddle around the rotor axis in a field. The torsional load of the dc servomotor is caused from resistance of the airflow over the moving paddle normal to the flow. The variations on the torsional load in one revolution of rotation can be characterized from the magnitude and direction of the airflow. In other words, the magnitude and direction of airflow cause a periodic function of the torsional load with respect to the angular position of the paddle. By using Fourier analysis, it is found that the magnitude and direction of the airflow can be determined from the coefficients of the Fourier series. Typically, the torsional load of the dc servomotor, unlike the rotor speed, cannot be measured by the built-in device. In this work, it is determined by applying the extended Luenberger observer method. A state-feedback controller with the observer based on $H2$ control design is implemented to regulate the dc servomotor. The experimental results on the measurement of airflow show the viability of the proposed methodology.

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